Pharmacophore matrix

According to these definitions, each atom of a molecule is assigned to no, one or two PPPs. Since the descriptor is based on atom pairs, a pharmacophore matrix is built up. The entries py of the pharmacophore matrix P hold the PPP pair of vertex i and vertex j. If an atom is not a member of any PPP group, the row and column that correspond to the atom remain empty. A single atom can also belong to more than one PPP group. In this case, the entry py of the pharmacophore matrix P holds more than one PPP pair. All possible pairing combinations of the five PPPs result in 15 pairs (DD, DA, DP, DN, DL, AA, AP, AN, AL, PP, PN, PL, NN, NL, LL). 

Linear representations are by far the most frequently used descriptor type. Apart from the already mentioned structural keys and hashed fingerprints, other types of information are stored. For example, the topological distance between pharmacophoric points can be stored [179, 180], auto- and cross-correlation vectors over 2-D or 3-D information can be created [185, 186], or so-called BCUT [187] values can be extracted from an eigenvalue analysis of the molecular adjacency matrix. 

Matrix metalloproteinase structural studies of the P -side inhibitors to date show a common set of inhibitor-enzyme interactions. This can be attributed primarily to the strong directional zinc-binding forces. Further stabilizing forces from the backbone hydrogen-bonding patterns common to a (3 sheet allow for minor adjustments due to the zinc interactions to be made while maintaining a common pharmacophore. 

DISCO considers three-dimensional conformations of compounds not as coordinates but as sets of interpoint distances, an approach similar to a distance geometry conformational search. Points are calculated between the coordinates of heavy atoms labeled with interaction functions such as HBD, HBA or hydrophobes. One atom can carry more than one label. The atom types are considered as far as they determine which interaction type the respective atom would be engaged in. The points of the hypothetical locations of the interaction counterparts in the receptor macromolecule also participate in the distance matrix. These are calculated from the idealized projections of the lone pairs of participating heavy atoms or H-bond forming hydrogens. The hydrophobic points are handled in a way that the hydrophobic matches are limited to, e.g., only one atom in a hydrophobic chain and there is a differentiation between aliphatic and aromatic hydrophobes. A minimum constraint on pharmacophore point of a certain type can be set, e.g. if a certain feature is known to be required for activity [53, 54]. 

MOE/QuaSAR Chemical Computing Group Inc. www.chemcomp.com/fdept/prodinfo.htm 2D (physical properties, subdivided surface areas, atom and bond counts, connectivity indices, adjacency and distance matrix descriptors, pharmacophore feature, partial charge descriptors), and 3D descriptors... 

The kinds of calculations described above are done for all the molecules under investigation and then all the data (combinations of 3-point pharmacophores) are stored in an X-matrix of descriptors suitable to be submitted for statistical analysis. In theory, every kind of statistical analysis and regression tool could be applied, however in this study we decided to focus on the linear regression model using principal component analysis (PCA) and partial least squares (PLS) (Fig. 4.9). PCA and PLS actually work very well in all those cases in which there are data with strongly collinear, noisy and numerous X-variables (Fig. 4.9). 

If the matrix is restricted to a subset of atoms, functional groups or pharmacophore centers shared by all molecules considered the matrices can be compared automatically by computer programs [86] (Fig. 11). However, this implies an atom-by-atom superposition of all atoms (or groups, or pharmacophore centers) that are part of the matrix. 

CFM = Compressed Feature Matrix —> substructure descriptors (0 pharmacophore-based descriptors)... 

Then, one ofthe most active compounds is chosen as the reference molecule and its ETMC (the template) is compared with all other ETMCs. By this comparison those matrix elements that are present in all active compounds but are absent in the inactive ones (i.e., active features or pharmacophore) are derived and represented by the Electronic-Topological Submatrix of Conjunction (ETSC). 

Another approach is based on the Compressed Feature Matrix (CFM), which is either a topological distance or geometrical distance matrix, whose elements represent distance relationships between atoms or pharmacophore types [Badreddin Abolmaah, Wegner et al., 2003]. 

Then, the Main Distance-Dependent Matrix (MDDM), for each pair of Interaction Pharmacophore Elements (IPEs) is estimated. The IPEs are specific and independent groups representing molecule functionality (Table Numerical Entriesl). The seventh IPE type (HS) encodes information about the overall molecular shape since all the nonhydrogen atoms are considered. From the MDDM estimated for the HS-HS pair, a similarity measure with respect to the whole molecule is obtained. 

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